Finite Group Databasebeta

← #9912912

Subgroups — #9912912

Order 512.

4855 conjugacy classes of subgroups.

The subgroup lattice has 1340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#58577C214yesmaximal, complemented
2#57168C214yesmaximal, complemented
3#56289C214yesmaximal, complemented
4#55314C214yesmaximal, complemented
5#55070C214yesmaximal, complemented
6#54953C214yesmaximal, complemented
7#53595C212yesmaximal, complemented
8#53391C214yesmaximal, complemented
9#53357C212yesmaximal, complemented
10#53176C214yesmaximal, complemented
11#51629C212yesmaximal, complemented
12#51067C212yesmaximal, complemented
13#49771C212yesmaximal, complemented
14#49562C212yesmaximal, complemented
15#48499C214yesmaximal, complemented
16#46237C211yesmaximal, characteristic, complemented
17#45962C212yesmaximal, complemented
18#45454C214yesmaximal, complemented
19#45453C212yesmaximal, complemented
20#38955C211yesmaximal, characteristic, complemented
21#37655C212yesmaximal, complemented
22#37269C212yesmaximal, complemented
23#37150C211yesmaximal, characteristic, complemented
24C2×#563C2211yescharacteristic
25C2×#562C2212yes—
26C2×H(3,𝔽4)C2211yescharacteristic
27C2×#554C2211yescharacteristic, complemented
28C2×#547C2211yescharacteristic
29C2×#535C2212yes—
30C2×#525C2212yes—
31C22×#123C2212yescomplemented
32#2862C2211yescharacteristic, complemented
33#2861C2212yescomplemented
34#2860C2212yescomplemented
35#2849C2212yescomplemented
36#2848C2214yescomplemented
37#2847C2214yes—
38#2837C2214yescomplemented
39#2830C2212yescomplemented
40#2829C2214yescomplemented
41#2828C2214yescomplemented
42#2828C2214yescomplemented
43#2820C2212yescomplemented
44#2816C2214yescomplemented
45#2814C2214yescomplemented
46#2814C2214yescomplemented
47#2813C2214yes—
48#2808C2212yescomplemented
49#2806C2212yescomplemented
50#2805C2212yescomplemented
51#2804C2212yescomplemented
52#2800C2214yescomplemented
53#2797C2214yescomplemented
54#2797C2214yescomplemented
55#2788C2214yescomplemented
56#2785C2212yescomplemented
57#2773C2214yescomplemented
58#2773C2214yescomplemented
59#2770C2214yescomplemented
60#2761C2214yescomplemented
61#2761C2214yescomplemented
62#2754C2214yescomplemented
63#2749C2214yescomplemented
64#2748C2214yescomplemented
65#2743C2214yescomplemented
66#2742C2214yescomplemented
67#2741C2214yescomplemented
68#2739C2214yescomplemented
69#2738C2214yescomplemented
70#2737C2214yescomplemented
71#2737C2214yescomplemented
72#2733C2212yes—
73#2733C2212yescomplemented
74#2732C2212yescomplemented
75#2731C2212yescomplemented
76#2730C2214yescomplemented
77#2730C2214yescomplemented
78#2728C2214yescomplemented
79#2728C2212yescomplemented
80#2723C2214yescomplemented
81#2715C2214yescomplemented
82#2715C2214yescomplemented
83#2714C2214yescomplemented
84#2712C2214yescomplemented
85#2710C2214yescomplemented
86#2709C2214yes—
87#2708C2214yescomplemented
88#2706C2214yescomplemented
89#2706C2214yescomplemented
90#2704C2214yescomplemented
91#2703C2214yescomplemented
92#2702C2214yescomplemented
93#2701C2214yescomplemented
94#2700C2214yescomplemented
95#2700C2214yescomplemented
96#2699C2212yes—
97#2699C2214yescomplemented
98#2697C2212yes—
99#2697C2212yes—
100#2696C2214yescomplemented
101#2696C2214yescomplemented
102#2694C2214yescomplemented
103#2693C2214yescomplemented
104#2692C2214yescomplemented
105#2691C2214yescomplemented
106#2687C2214yescomplemented
107#2687C2214yescomplemented
108#2687C2214yescomplemented
109#2686C2214yes—
110#2686C2214yescomplemented
111#2685C2214yescomplemented
112#2685C2214yescomplemented
113#2685C2214yescomplemented
114#2684C2212yes—
115#2684C2214yescomplemented
116#2683C2211yescharacteristic
117#2683C2214yescomplemented
118#2682C2214yes—
119#2682C2212yes—
120#2682C2212yescomplemented
121#2681C2214yescomplemented
122#2681C2214yescomplemented
123#2681C2214yescomplemented
124#2679C2211yescharacteristic
125#2679C2212yes—
126#2677C2214yescomplemented
127#2676C2214yescomplemented
128#2676C2214yescomplemented
129#2674C2214yescomplemented
130#2674C2214yescomplemented
131#2673C2214yes—
132#2672C2214yescomplemented
133#2671C2214yes—
134#2670C2214yescomplemented
135#2669C2214yes—
136#2669C2214yes—
137#2668C2214yescomplemented
138#2668C2214yescomplemented
139#2666C2214yescomplemented
140#2665C2214yescomplemented
141#2661C2214yescomplemented
142#2651C2214yescomplemented
143#2638C2214yescomplemented
144#2635C2214yescomplemented
145#2632C2212yescomplemented
146#2631C2212yescomplemented
147#2624C2214yes—
148#2621C2212yescomplemented
149#2617C2212yescomplemented
150#2617C2214yescomplemented
151#2613C2212yescomplemented
152#2596C2214yescomplemented
153#2595C2214yescomplemented
154#2593C2214yescomplemented
155#2590C2214yescomplemented
156#2586C2212yescomplemented
157#2578C2214yescomplemented
158#2563C2211yescharacteristic
159#2555C2214yescomplemented
160#2546C2211yescharacteristic, complemented
161#2545C2212yescomplemented
162#2544C2214yes—
163#2540C2214yescomplemented
164#2540C2212yescomplemented
165#2539C2212yescomplemented
166#2534C2212yes—
167#2534C2214yescomplemented
168#2522C2214yescomplemented
169#2521C2214yescomplemented
170#2518C2214yescomplemented
171#2518C2214yescomplemented
172#2516C2214yescomplemented
173#2503C2212yescomplemented
174#2491C2214yescomplemented
175#2485C2214yescomplemented
176#2478C2214yescomplemented
177#2474C2214yescomplemented
178#2472C2214yescomplemented
179#2472C2214yescomplemented
180#2472C2214yescomplemented
181#2470C2214yescomplemented
182#2468C2214yescomplemented
183#2463C2214yescomplemented
184#2461C2214yescomplemented
185#2460C2214yescomplemented
186#2456C2214yescomplemented
187#2456C2214yescomplemented
188#2452C2214yescomplemented
189#2449C2214yescomplemented
190#2449C2214yescomplemented
191#2445C2214yes—
192#2443C2214yes—
193#2442C2214yescomplemented
194#2437C2214yescomplemented
195#2432C2212yes—
196#2424C2214yes—
197#2420C2214yescomplemented
198#2420C2214yescomplemented
199#2418C2214yescomplemented
200#2417C2214yescomplemented
201#2416C2214yescomplemented
202#2414C2214yescomplemented
203#2413C2212yescomplemented
204#2412C2214yescomplemented
205#2411C2212yescomplemented
206#2410C2214yescomplemented
207#2408C2214yescomplemented
208#2406C2212yes—
209#2404C2212yes—
210#2376C2212yes—
211#2376C2214yescomplemented
212#2358C2212yes—
213#2344C2212yescomplemented
214#2336C2212yescomplemented
215#2321C2212yes—
216#2311C2212yes—
217C4×#124C2211yescharacteristic
218#2293C2211yescharacteristic, complemented
219C22×#41C2312yes—
220C23×D4C2312yes—
221C24×C4C2312yes—
222#563—44no—
223#562—48no—
224H(3,𝔽4)—44no—
225#554—44no—
226#547—44no—
227#535—48no—
228C2×C4⋊Q8C2311yescharacteristic
229C2×C4⋊Q8C2311yescharacteristic
230C2×C4⋊Q8C2312yes—
231C2×C4⋊Q8C2312yes—
232C2×#127C2314yes—
233C2×#126C2314yes—
234C2×#126C2314yes—
235C2×#125C2312yes—
236C2×#125C2312yes—
237C2×#124C2311yescharacteristic
238C2×#124C2312yes—
239C2×#124C2312yes—
240C2×#124C2312yes—
241C2×#124C2314yes—
242C2×#124C2314yes—
243C2×#124C2312yes—
244C2×#124C2314yes—
245C2×#124C2314yes—
246#525—48no—
247C2×#123—48no—
248C2×#123C2312yes—
249C2×#123C2314yes—
250C2×#123C2312yes—
251C2×#123C2312yes—
252C2×#123C2314yes—
253C2×#123C2314yes—
254C2×#123C2314yes—
255C2×#123C2312yes—
256C2×#123C2314yes—
257C2×#123C2312yes—
258C2×#123C2314yes—
259C2×C22⋊Q8C2314yes—
260C2×C22⋊Q8C2314yes—
261C2×C22⋊Q8C2312yes—
262C2×C22⋊Q8C2312yes—
263C2×C22⋊Q8C2314yes—
264C2×C22⋊Q8C2314yes—
265C2×C22⋊Q8C2314yes—
266C2×C22⋊Q8C2314yes—
267C2×C22⋊Q8C2314yes—
268C2×C22⋊Q8C2314yes—
269C2×C22⋊Q8C2314yes—
270C2×#121C2314yes—
271C2×#121C2314yes—
272C2×#121C2312yes—
273C2×#121C2314yes—
274C2×#121C2314yes—
275C2×#121C2314yes—
276C2×#121C2314yes—
277C2×#121C2314yes—
278C2×#121C2314yes—
279C2×#121C2314yes—
280C2×#121C2314yes—
281C2×#120C2312yes—
282C2×#120C2312yes—
283C2×#120C2312yes—
284C2×#120C2312yes—
285C2×#120C2312yes—
286C2×#120C2314yes—
287C2×#120C2314yes—
288C2×#120C2314yes—
289C2×#120C2312yes—
290C2×#120C2314yes—
291C2×C4×Q8C2311yescharacteristic
292C2×C4×D4C2311yescharacteristic
293C2×C4×D4C2311yescharacteristic
294C2×C4×D4C2312yes—
295C2×C4×D4C2314yes—
296C2×C4×D4C2314yes—
297C2×C4×D4C2314yes—
298C2×C4×D4C2314yes—
299C2×#117C2312yes—
300C2×#117C2312yes—
301C2×#117C2312yes—
302C22×C4⋊C4C2312yes—
303C22×C4⋊C4C2312yes—
304C22×C4⋊C4C2312yes—
305C22×C22⋊C4C2312yes—
306C22×C22⋊C4C2312yes—
307C22×C22⋊C4C2312yes—
308C22×C22⋊C4C2314yes—
309#400C2314yes—
310#400C2314yes—
311#400C2314yes—
312#400C2314yes—
313#400C2314yes—
314#400C2314yes—
315#400C2314yes—
316#400C2314yes—
317#399C2314yes—
318#399C2314yes—
319#399C2314yes—
320#399C2314yes—
321#399C2314yes—
322#399C2314yes—
323#399C2314yes—
324#399C2314yes—
325#398C2314yes—
326#398C2314yes—
327#398C2314yes—
328#398C2312yes—
329#398C2312yes—
330#398C2314yes—
331#398C2314yes—
332#398C2314yes—
333#398C2314yes—
334#398C2314yes—
335#398C2314yes—
336#398C2314yes—
337#398C2314yes—
338#397C2314yes—
339#397C2314yes—
340#397C2314yes—
341#397C2314yes—
342#397C2314yes—
343#397C2314yes—
344#397C2314yes—
345#397C2314yes—
346#397C2314yes—
347#397C2314yes—
348#397C2314yes—
349#397C2314yes—
350#397C2314yes—
351#397C2314yes—
352#397C2314yes—
353#397C2314yes—
354#397C2314yes—
355#397C2314yes—
356#397C2314yes—
357#396C2314yes—
358#396C2314yes—
359#396C2314yes—
360#396C2314yes—
361#396C2314yes—
362#396C2314yes—
363#396C2314yes—
364#396C2314yes—
365#396C2314yes—
366#396C2314yes—
367#396C2314yes—
368#396C2314yes—
369#396C2314yes—
370#396C2314yes—
371#395C2314yes—
372#395C2312yes—
373#395C2314yes—
374#395C2312yes—
375#395C2314yes—
376#395C2314yes—
377#395C2314yes—
378#394C2314yes—
379#394C2314yes—
380#394C2314yes—
381#394C2314yes—
382#394C2314yes—
383#394C2314yes—
384#394C2314yes—
385#394C2314yes—
386#394C2314yes—
387#394C2314yes—
388#394C2314yes—
389#394C2314yes—
390#394C2314yes—
391#394C2314yes—
392#394C2314yes—
393#394C2314yes—
394#394C2314yes—
395#394C2314yes—
396#394C2314yes—
397#394C2314yes—
398#394C2314yes—
399#394C2314yes—
400#394C2314yes—
401#394C2314yes—
402#394C2314yes—
403#394C2314yes—
404#394C2312yes—
405#394C2312yes—
406#394C2314yes—
407#394C2314yes—
408#394C2314yes—
409#394C2314yes—
410#394C2314yes—
411#394C2314yes—
412#394C2314yes—
413#394C2314yes—
414#394C2314yes—
415#393C2314yes—
416#393C2314yes—
417#393C2314yes—
418#393C2314yes—
419#393C2314yes—
420#393C2314yes—
421#393C2314yes—
422#393C2314yes—
423#393C2314yes—
424#392C2314yes—
425#392C2314yes—
426#392C2314yes—
427#392C2314yes—
428#392C2314yes—
429#392C2314yes—
430#392C2314yes—
431#392C2314yes—
432#392C2314yes—
433#392C2314yes—
434#392C2314yes—
435#392C2314yes—
436#392C2314yes—
437#392C2314yes—
438#391C2312yes—
439#391C2312yes—
440#391C2314yes—
441#391C2312yes—
442#391C2312yes—
443#391C2312yes—
444#391C2312yes—
445#391C2312yes—
446#391C2312yes—
447#391C2311yescharacteristic
448#391C2314yes—
449#390C2312yes—
450#390C2311yescharacteristic
451#390C2312yes—
452#390C2314yes—
453#390C2314yes—
454#390C2312yes—
455#390C2314yes—
456#390C2314yes—
457#390C2314yes—
458#390C2312yes—
459#390C2312yes—
460#390C2312yes—
461#390C2312yes—
462#390C2312yes—
463#390C2314yes—
464#390C2314yes—
465#390C2314yes—
466#390C2314yes—
467#390C2314yes—
468#390C2314yes—
469#389C2314yes—
470#389C2314yes—
471#389C2314yes—
472#389C2314yes—
473#389C2314yes—
474#389C2314yes—
475#389C2314yes—
476#389C2312yes—
477#389C2312yes—
478#389C2312yes—
479#389C2314yes—
480#389C2312yes—
481#389C2314yes—
482#388C2314yes—
483#388C2314yes—
484#388C2314yes—
485#388C2314yes—
486#388C2314yes—
487#388C2314yes—
488#388C2314yes—
489#388C2314yes—
490#388C2314yes—
491#388C2314yes—
492#388C2314yes—
493#388C2314yes—
494#388C2314yes—
495#388C2314yes—
496#388C2314yes—
497#388C2314yes—
498#388C2314yes—
499#388C2314yes—
500#388C2314yes—
501#388C2314yes—
502#388C2314yes—
503#388C2314yes—
504#388C2314yes—
505#388C2314yes—
506#388C2314yes—
507#388C2314yes—
508#388C2314yes—
509#388C2314yes—
510#388C2314yes—
511#388C2314yes—
512#388C2314yes—
513#388C2314yes—
514#388C2314yes—
515#388C2314yes—
516#388C2314yes—
517#387C2314yes—
518#387C2314yes—
519#387C2314yes—
520#387C2314yes—
521#387C2314yes—
522#387C2314yes—
523#387C2314yes—
524#387C2314yes—
525#387C2314yes—
526#387C2314yes—
527#387C2314yes—
528#387C2314yes—
529#387C2314yes—
530#387C2314yes—
531#387C2314yes—
532#387C2314yes—
533#387C2314yes—
534#387C2314yes—
535#386C2314yes—
536#386C2314yes—
537#386C2312yes—
538#386C2314yes—
539#386C2314yes—
540#386C2314yes—
541#386C2314yes—
542#386C2314yes—
543#386C2314yes—
544#386C2314yes—
545#386C2314yes—
546#386C2314yes—
547#386C2314yes—
548#386C2314yes—
549#386C2314yes—
550#386C2312yes—
551#386C2312yes—
552#386C2314yes—
553#386C2314yes—
554#386C2314yes—
555#386C2314yes—
556#386C2314yes—
557#386C2314yes—
558#386C2314yes—
559#386C2314yes—
560#386C2314yes—
561#386C2314yes—
562#386C2314yes—
563#386C2314yes—
564#385C2312yes—
565#385C2314yes—
566#385C2314yes—
567#385C2314yes—
568#385C2314yes—
569#385C2314yes—
570#385C2314yes—
571#385C2314yes—
572#385C2314yes—
573#385C2314yes—
574#385C2314yes—
575#385C2314yes—
576#385C2314yes—
577#385C2314yes—
578#385C2314yes—
579#385C2314yes—
580#385C2314yes—
581#383C2314yes—
582#383C2312yes—
583#382C2312yes—
584#382C2311yescharacteristic
585#382C2314yes—
586#382C2314yes—
587#381C2314yes—
588#381C2312yes—
589#381C2312yes—
590#381C2312yes—
591#381C2314yes—
592#381C2314yes—
593#381C2314yes—
594#380C2314yes—
595#380C2314yes—
596#380C2314yes—
597#380C2314yes—
598#380C2314yes—
599#380C2314yes—
600#380C2314yes—
601#380C2314yes—
602#380C2312yes—
603#380C2314yes—
604#380C2314yes—
605#380C2314yes—
606#379C2312yes—
607#379C2314yes—
608#379C2314yes—
609#379C2312yes—
610#379C2314yes—
611C4×C4⋊C4C2311yescharacteristic
612C4×C4⋊C4C2314yes—
613C4×C4⋊C4C2314yes—
614C4×C4⋊C4C2314yes—
615C4×C4⋊C4C2312yes—
616C4×C22⋊C4C2312yes—
617C4×C22⋊C4C2314yes—
618C4×C22⋊C4C2314yes—
619C4×C22⋊C4C2314yes—
620C4×C22⋊C4C2312yes—
621C43C2311yescharacteristic
622C25C2412yes—
623C25C2412yes—
624C2×#41—28no—
625C2×#41—44no—
626C2×#41—82no—
627C22×Q8C2411yescharacteristic
628C22×Q8C2412yes—
629C22×Q8C2412yes—
630C22×Q8C2412yes—
631C22×Q8C2412yes—
632C22×Q8C2412yes—
633C22×D4—44no—
634C22×D4—44no—
635C22×D4—82no—
636C22×D4C2411yescharacteristic
637C22×D4C2414yes—
638C22×D4C2414yes—
639C22×D4C2412yes—
640C22×D4C2412yes—
641C22×D4C2414yes—
642C22×D4C2414yes—
643C22×D4C2414yes—
644C22×D4C2412yes—
645C22×D4C2412yes—
646C22×D4C2414yes—
647C22×D4C2412yes—
648C22×D4C2414yes—
649C22×D4C2412yes—
650C22×D4C2414yes—
651C22×D4C2414yes—
652C22×D4C2414yes—
653C22×D4C2411yescharacteristic
654C23×C4—44no—
655C23×C4—44no—
656C23×C4—82no—
657C23×C4C2412yes—
658C23×C4C2412yes—
659C23×C4C2412yes—
660C23×C4C2412yes—
661C23×C4C2412yes—
662C23×C4C2414yes—
663C23×C4C2412yes—
664C23×C4C2414yes—
665C23×C4C2414yes—
666C23×C4C2414yes—
667C23×C4C2414yes—
668C4⋊Q8—42no—
669C4⋊Q8—42no—
670C4⋊Q8—44no—
671C4⋊Q8—82no—
672#127—48no—
673#126—48no—
674#126—84no—
675#125—28no—
676#125—44no—
677#124—24no—
678#124—44no—
679#124—44no—
680#124—44no—
681#124—48no—
682#124—48no—
683#124—44no—
684#124—84no—
685#124—84no—
686#123—28no—
687#123—216no—
688#123—48no—
689#123—48no—
690#123—48no—
691#123—44no—
692#123—44no—
693#123—44no—
694#123—48no—
695#123—84no—
696#123—82no—
697C22⋊Q8—48no—
698C22⋊Q8—48no—
699C22⋊Q8—48no—
700C22⋊Q8—48no—
701C22⋊Q8—44no—
702C22⋊Q8—44no—
703C22⋊Q8—48no—
704C22⋊Q8—84no—
705C22⋊Q8—84no—
706C22⋊Q8—84no—
707C22⋊Q8—84no—
708#121—48no—
709#121—48no—
710#121—48no—
711#121—44no—
712#121—48no—
713#121—48no—
714#121—84no—
715#121—84no—
716#121—84no—
717#121—84no—
718#121—84no—
719#120—28no—
720#120—28no—
721#120—44no—
722#120—44no—
723#120—44no—
724#120—48no—
725#120—84no—
726#120—84no—
727#120—82no—
728#120—84no—
729C4×Q8—42no—
730C4×D4—24no—
731C4×D4—44no—
732C4×D4—42no—
733C4×D4—48no—
734C4×D4—48no—
735C4×D4—84no—
736C4×D4—84no—
737#117—44no—
738#117—44no—
739#117—82no—
740C2×C4⋊C4—28no—
741C2×C4⋊C4—44no—
742C2×C4⋊C4—44no—
743C2×C4⋊C4C2414yes—
744C2×C4⋊C4C2412yes—
745C2×C4⋊C4C2414yes—
746C2×C4⋊C4C2412yes—
747C2×C4⋊C4C2412yes—
748C2×C4⋊C4C2414yes—
749C2×C4⋊C4C2412yes—
750C2×C4⋊C4C2414yes—
751C2×C4⋊C4C2411yescharacteristic
752C2×C4⋊C4C2412yes—
753C2×C4⋊C4C2414yes—
754C2×C4⋊C4C2414yes—
755C2×C4⋊C4C2414yes—
756C2×C4⋊C4C2414yes—
757C2×C4⋊C4C2411yescharacteristic
758C2×C4⋊C4C2414yes—
759C2×C4⋊C4C2414yes—
760C2×C4⋊C4C2414yes—
761C2×C4⋊C4C2412yes—
762C2×C4⋊C4C2414yes—
763C2×C4⋊C4C2414yes—
764C2×C4⋊C4C2414yes—
765C2×C4⋊C4C2414yes—
766C2×C4⋊C4C2414yes—
767C2×C4⋊C4C2412yes—
768C2×C4⋊C4C2414yes—
769C2×C4⋊C4C2412yes—
770C2×C4⋊C4C2414yes—
771C2×C4⋊C4C2414yes—
772C2×C4⋊C4C2414yes—
773C2×C4⋊C4C2414yes—
774C2×C4⋊C4C2414yes—
775C2×C4⋊C4C2414yes—
776C2×C4⋊C4C2414yes—
777C2×C4⋊C4C2411yescharacteristic
778C2×C4⋊C4C2411yescharacteristic
779C2×C4⋊C4C2412yes—
780C2×C4⋊C4C2412yes—
781C2×C4⋊C4C2412yes—
782C2×C4⋊C4C2414yes—
783C2×C4⋊C4C2414yes—
784C2×C4⋊C4C2412yes—
785C2×C4⋊C4C2411yescharacteristic
786C2×C22⋊C4—44no—
787C2×C22⋊C4—44no—
788C2×C22⋊C4—44no—
789C2×C22⋊C4—84no—
790C2×C22⋊C4C2414yes—
791C2×C22⋊C4C2414yes—
792C2×C22⋊C4C2414yes—
793C2×C22⋊C4C2412yes—
794C2×C22⋊C4C2412yes—
795C2×C22⋊C4C2412yes—
796C2×C22⋊C4C2414yes—
797C2×C22⋊C4C2414yes—
798C2×C22⋊C4C2412yes—
799C2×C22⋊C4C2414yes—
800C2×C22⋊C4C2414yes—
801C2×C22⋊C4C2414yes—
802C2×C22⋊C4C2414yes—
803C2×C22⋊C4C2414yes—
804C2×C22⋊C4C2414yes—
805C2×C22⋊C4C2414yes—
806C2×C22⋊C4C2414yes—
807C2×C22⋊C4C2414yes—
808C2×C22⋊C4C2414yes—
809C2×C22⋊C4C2414yes—
810C2×C22⋊C4C2414yes—
811C2×C22⋊C4C2414yes—
812C2×C22⋊C4C2414yes—
813C2×C22⋊C4C2414yes—
814C2×C22⋊C4C2414yes—
815C2×C22⋊C4C2412yes—
816C2×C22⋊C4C2414yes—
817C2×C22⋊C4C2414yes—
818C2×C22⋊C4C2414yes—
819C2×C22⋊C4C2414yes—
820C2×C22⋊C4C2414yes—
821C2×C22⋊C4C2414yes—
822C2×C22⋊C4C2414yes—
823C2×C22⋊C4C2414yes—
824C2×C22⋊C4C2412yes—
825C2×C22⋊C4C2414yes—
826C2×C22⋊C4C2414yes—
827C2×C22⋊C4C2414yes—
828C2×C22⋊C4C2414yes—
829C2×C22⋊C4C2414yes—
830C2×C22⋊C4C2412yes—
831C2×C22⋊C4C2412yes—
832C2×C22⋊C4C2414yes—
833C2×C22⋊C4C2414yes—
834C2×C22⋊C4C2414yes—
835C2×C22⋊C4C2414yes—
836C2×C22⋊C4C2414yes—
837C2×C22⋊C4C2414yes—
838C2×C22⋊C4C2414yes—
839C2×C22⋊C4C2414yes—
840C2×C22⋊C4C2414yes—
841C2×C22⋊C4C2414yes—
842C2×C22⋊C4C2414yes—
843C2×C22⋊C4C2414yes—
844C2×C22⋊C4C2414yes—
845C2×C22⋊C4C2414yes—
846C2×C22⋊C4C2414yes—
847C2×C22⋊C4C2414yes—
848C2×C22⋊C4C2414yes—
849C2×C42C2411yescharacteristic
850C2×C42C2412yes—
851C2×C42C2411yescharacteristic
852C2×C42C2411yescharacteristic
853C2×C42C2414yes—
854C2×C42C2414yes—
855C2×C42C2412yes—
856C2×C42C2414yes—
857C2×C42C2414yes—
858C2×C42C2412yes—
859C2×C42C2412yes—
860C2×C42C2412yes—
861C2×C42C2412yes—
862C2×C42C2414yes—
863#95C2414yes—
864#95C2414yes—
865#95C2414yes—
866#95C2414yes—
867#95C2414yes—
868#95C2414yes—
869#95C2414yes—
870#95C2414yes—
871#95C2414yes—
872#95C2414yes—
873#95C2414yes—
874#95C2414yes—
875#95C2414yes—
876#95C2414yes—
877#95C2412yes—
878#95C2414yes—
879#95C2414yes—
880#95C2414yes—
881#95C2414yes—
882#95C2414yes—
883#95C2414yes—
884#95C2414yes—
885#95C2414yes—
886#95C2414yes—
887#95C2414yes—
888#95C2414yes—
889#95C2414yes—
890#95C2414yes—
891#95C2414yes—
892#95C2414yes—
893#95C2412yes—
894#95C2414yes—
895#95C2414yes—
896#95C2414yes—
897#95C2414yes—
898#95C2414yes—
899#95C2412yes—
900#95C2414yes—
901#95C2414yes—
902#95C2414yes—
903#95C2414yes—
904#95C2414yes—
905C24—24no—
906C24—24no—
907C24—42no—
908C24—42no—
909C24—42no—
910C24—44no—
911C24—44no—
912C24—44no—
913C24—44no—
914C24—42no—
915C24C2514yes—
916C24C2514yes—
917C24C2512yes—
918C24C2512yes—
919#41—816no—
920C2×Q8—24no—
921C2×Q8—22no—
922C2×Q8—41no—
923C2×Q8—42no—
924C2×Q8—41no—
925C2×Q8—42no—
926C2×Q8—42no—
927C2×Q8—42no—
928C2×Q8—42no—
929C2×Q8—42no—
930C2×Q8—42no—
931C2×Q8—44no—
932C2×Q8—42no—
933C2×Q8—42no—
934C2×Q8—42no—
935C2×Q8—42no—
936C2×Q8—42no—
937C2×D4—28no—
938C2×D4—28no—
939C2×D4—24no—
940C2×D4—24no—
941C2×D4—22no—
942C2×D4—28no—
943C2×D4—41no—
944C2×D4—42no—
945C2×D4—41no—
946C2×D4—44no—
947C2×D4—44no—
948C2×D4—44no—
949C2×D4—44no—
950C2×D4—44no—
951C2×D4—42no—
952C2×D4—44no—
953C2×D4—42no—
954C2×D4—42no—
955C2×D4—44no—
956C2×D4—44no—
957C2×D4—44no—
958C2×D4—44no—
959C2×D4—42no—
960C2×D4—44no—
961C2×D4—44no—
962C2×D4—44no—
963C2×D4—44no—
964C2×D4—44no—
965C2×D4—42no—
966C2×D4—42no—
967C2×D4—44no—
968C2×D4—44no—
969C2×D4—44no—
970C2×D4—42no—
971C2×D4—44no—
972C2×D4—44no—
973C2×D4—44no—
974C2×D4—44no—
975C2×D4—42no—
976C2×D4—42no—
977C2×D4—42no—
978C2×D4—42no—
979C2×D4—44no—
980C2×D4—44no—
981C2×D4—42no—
982C2×D4—44no—
983C2×D4—42no—
984C2×D4—42no—
985C2×D4—44no—
986C2×D4—44no—
987C2×D4—44no—
988C2×D4—816no—
989C2×D4H(5,𝔽2)14yes—
990C22×C4—24no—
991C22×C4—24no—
992C22×C4—24no—
993C22×C4—24no—
994C22×C4—24no—
995C22×C4—24no—
996C22×C4—24no—
997C22×C4—24no—
998C22×C4—28no—
999C22×C4—42no—
1000C22×C4—42no—
1001C22×C4—42no—
1002C22×C4—42no—
1003C22×C4—42no—
1004C22×C4—44no—
1005C22×C4—44no—
1006C22×C4—44no—
1007C22×C4—44no—
1008C22×C4—44no—
1009C22×C4—44no—
1010C22×C4—42no—
1011C22×C4—44no—
1012C22×C4—44no—
1013C22×C4—44no—
1014C22×C4—44no—
1015C22×C4—44no—
1016C22×C4—44no—
1017C22×C4—44no—
1018C22×C4—44no—
1019C22×C4—44no—
1020C22×C4—44no—
1021C22×C4—816no—
1022C22×C4C2514yes—
1023C22×C4C2512yes—
1024C22×C4C2514yes—
1025C22×C4C2514yes—
1026C22×C4C2512yes—
1027C22×C4C2512yes—
1028C22×C4C2514yes—
1029C22×C4C2512yes—
1030C22×C4C2512yes—
1031C22×C4C2514yes—
1032C22×C4C2512yes—
1033C22×C4C2514yes—
1034C22×C4C2514yes—
1035C22×C4C2514yes—
1036C22×C4C2511yescharacteristic
1037C22×C4C2512yes—
1038C22×C4C2511yescharacteristic
1039C22×C4C2512yes—
1040C22×C4C2511yescharacteristic
1041C4⋊C4—24no—
1042C4⋊C4—24no—
1043C4⋊C4—24no—
1044C4⋊C4—28no—
1045C4⋊C4—28no—
1046C4⋊C4—28no—
1047C4⋊C4—24no—
1048C4⋊C4—28no—
1049C4⋊C4—41no—
1050C4⋊C4—42no—
1051C4⋊C4—44no—
1052C4⋊C4—42no—
1053C4⋊C4—44no—
1054C4⋊C4—42no—
1055C4⋊C4—44no—
1056C4⋊C4—44no—
1057C4⋊C4—44no—
1058C4⋊C4—44no—
1059C4⋊C4—41no—
1060C4⋊C4—44no—
1061C4⋊C4—44no—
1062C4⋊C4—44no—
1063C4⋊C4—42no—
1064C4⋊C4—44no—
1065C4⋊C4—44no—
1066C4⋊C4—44no—
1067C4⋊C4—44no—
1068C4⋊C4—44no—
1069C4⋊C4—42no—
1070C4⋊C4—44no—
1071C4⋊C4—44no—
1072C4⋊C4—44no—
1073C4⋊C4—42no—
1074C4⋊C4—44no—
1075C4⋊C4—44no—
1076C4⋊C4—44no—
1077C4⋊C4—44no—
1078C4⋊C4—44no—
1079C4⋊C4—41no—
1080C4⋊C4—41no—
1081C4⋊C4—42no—
1082C4⋊C4—42no—
1083C4⋊C4H(5,𝔽2)14yes—
1084C22⋊C4—24no—
1085C22⋊C4—24no—
1086C22⋊C4—24no—
1087C22⋊C4—28no—
1088C22⋊C4—28no—
1089C22⋊C4—28no—
1090C22⋊C4—28no—
1091C22⋊C4—28no—
1092C22⋊C4—24no—
1093C22⋊C4—28no—
1094C22⋊C4—28no—
1095C22⋊C4—44no—
1096C22⋊C4—44no—
1097C22⋊C4—44no—
1098C22⋊C4—44no—
1099C22⋊C4—44no—
1100C22⋊C4—44no—
1101C22⋊C4—44no—
1102C22⋊C4—44no—
1103C22⋊C4—44no—
1104C22⋊C4—44no—
1105C22⋊C4—44no—
1106C22⋊C4—44no—
1107C22⋊C4—44no—
1108C22⋊C4—44no—
1109C22⋊C4—44no—
1110C22⋊C4—44no—
1111C22⋊C4—42no—
1112C22⋊C4—44no—
1113C22⋊C4—44no—
1114C22⋊C4—44no—
1115C22⋊C4—44no—
1116C22⋊C4—44no—
1117C22⋊C4—44no—
1118C22⋊C4—44no—
1119C22⋊C4—44no—
1120C22⋊C4—44no—
1121C22⋊C4—44no—
1122C22⋊C4—44no—
1123C22⋊C4—44no—
1124C22⋊C4—44no—
1125C22⋊C4—42no—
1126C22⋊C4—44no—
1127C22⋊C4—44no—
1128C22⋊C4—44no—
1129C22⋊C4—42no—
1130C22⋊C4—42no—
1131C22⋊C4—44no—
1132C22⋊C4—44no—
1133C22⋊C4—44no—
1134C22⋊C4—44no—
1135C22⋊C4—44no—
1136C22⋊C4—44no—
1137C22⋊C4—44no—
1138C22⋊C4—44no—
1139C22⋊C4—44no—
1140C22⋊C4—44no—
1141C22⋊C4—44no—
1142C22⋊C4—44no—
1143C42—22no—
1144C42—24no—
1145C42—22no—
1146C42—42no—
1147C42—44no—
1148C42—44no—
1149C42—44no—
1150C42—41no—
1151C42—42no—
1152C42—44no—
1153C42—44no—
1154C42—42no—
1155C42—42no—
1156C42—42no—
1157C23—22no—
1158C23—24no—
1159C23—22no—
1160C23—24no—
1161C23—24no—
1162C23—22no—
1163C23—24no—
1164C23—24no—
1165C23—24no—
1166C23—22no—
1167C23—24no—
1168C23—22no—
1169C23—24no—
1170C23—24no—
1171C23—24no—
1172C23—24no—
1173C23—24no—
1174C23—24no—
1175C23—24no—
1176C23—24no—
1177C23—24no—
1178C23—24no—
1179C23—24no—
1180C23—48no—
1181C23—88no—
1182C23—84no—
1183C23—88no—
1184C23—84no—
1185C23—84no—
1186C23—88no—
1187C23—84no—
1188C23—84no—
1189C23—164no—
1190C23C2×H(5,𝔽2)14yes—
1191C23C2611yescharacteristic
1192Q8—82no—
1193Q8—84no—
1194Q8—162no—
1195Q8—162no—
1196Q8—162no—
1197Q8—162no—
1198D4—44no—
1199D4—44no—
1200D4—88no—
1201D4—88no—
1202D4—88no—
1203D4—84no—
1204D4—84no—
1205D4—88no—
1206D4—88no—
1207D4—88no—
1208D4—164no—
1209D4—164no—
1210D4—162no—
1211D4—164no—
1212D4—162no—
1213D4—162no—
1214D4—164no—
1215D4—162no—
1216C2×C4—21no—
1217C2×C4—22no—
1218C2×C4—21no—
1219C2×C4—22no—
1220C2×C4—22no—
1221C2×C4—22no—
1222C2×C4—21no—
1223C2×C4—22no—
1224C2×C4—22no—
1225C2×C4—24no—
1226C2×C4—24no—
1227C2×C4—22no—
1228C2×C4—24no—
1229C2×C4—22no—
1230C2×C4—24no—
1231C2×C4—24no—
1232C2×C4—24no—
1233C2×C4—22no—
1234C2×C4—22no—
1235C2×C4—22no—
1236C2×C4—24no—
1237C2×C4—22no—
1238C2×C4—24no—
1239C2×C4—24no—
1240C2×C4—22no—
1241C2×C4—22no—
1242C2×C4—22no—
1243C2×C4—22no—
1244C2×C4—24no—
1245C2×C4—24no—
1246C2×C4—24no—
1247C2×C4—24no—
1248C2×C4—24no—
1249C2×C4—24no—
1250C2×C4—24no—
1251C2×C4—24no—
1252C2×C4—24no—
1253C2×C4—24no—
1254C2×C4—22no—
1255C2×C4—24no—
1256C2×C4—22no—
1257C2×C4—22no—
1258C2×C4—24no—
1259C2×C4—22no—
1260C2×C4—24no—
1261C2×C4—22no—
1262C2×C4—24no—
1263C2×C4—24no—
1264C2×C4—24no—
1265C2×C4—24no—
1266C2×C4—48no—
1267C2×C4—48no—
1268C2×C4—48no—
1269C2×C4—84no—
1270C2×C4—88no—
1271C2×C4—84no—
1272C2×C4—84no—
1273C2×C4—88no—
1274C2×C4—164no—
1275C2×C4—164no—
1276C2×C4—164no—
1277C2×C4C2×H(5,𝔽2)12yes—
1278C2×C4C2×H(5,𝔽2)12yes—
1279C2×C4C2×H(5,𝔽2)14yes—
1280C22—28no—
1281C22—24no—
1282C22—42no—
1283C22—42no—
1284C22—44no—
1285C22—44no—
1286C22—44no—
1287C22—44no—
1288C22—44no—
1289C22—44no—
1290C22—42no—
1291C22—44no—
1292C22—44no—
1293C22—42no—
1294C22—44no—
1295C22—44no—
1296C22—42no—
1297C22—44no—
1298C22—44no—
1299C22—44no—
1300C22—44no—
1301C22—44no—
1302C22—44no—
1303C22—44no—
1304C22—816no—
1305C22—168no—
1306C22C22×H(5,𝔽2)11yescharacteristic
1307C22C22×H(5,𝔽2)11yescharacteristic
1308C22H(7,𝔽2)12yes—
1309C22H(7,𝔽2)11yescharacteristic
1310C222−1+612yes—
1311C4—22no—
1312C4—24no—
1313C4—22no—
1314C4—44no—
1315C4—44no—
1316C4—44no—
1317C4—42no—
1318C4—44no—
1319C4—42no—
1320C4—44no—
1321C4—41no—
1322C4—42no—
1323C4—42no—
1324C4—42no—
1325C4—44no—
1326C4—42no—
1327C4—44no—
1328C4—44no—
1329C4—42no—
1330C2—44no—
1331C2—82no—
1332C2—84no—
1333C2—84no—
1334C2#6288611yescharacteristic
1335C2#6289211yescharacteristic
1336C2#6297412yes—
1337C2#6304912yes—
1338C2#6306611yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #58577C2semidirect
2. #57168C2semidirect
3. #56289C2semidirect
4. #55314C2semidirect
5. #55070C2semidirect
6. #54953C2semidirect
7. #53595C2semidirect
8. #53391C2semidirect
9. #53357C2semidirect
10. #53176C2semidirect
11. #51629C2semidirect
12. #51067C2semidirect
13. #49771C2semidirect
14. #49562C2semidirect
15. #48499C2semidirect
16. #46237C2semidirect
17. #45962C2semidirect
18. #45454C2semidirect
19. #45453C2semidirect
20. #38955C2semidirect
21. #37655C2semidirect
22. #37269C2semidirect
23. #37150C2semidirect
27. C2×#554C22semidirect
31. C22×#123C22semidirect
32. #2862C22semidirect
33. #2861C22semidirect
34. #2860C22semidirect
35. #2849C22semidirect
36. #2848C22semidirect
38. #2837C22semidirect
39. #2830C22semidirect
40. #2829C22semidirect
41. #2828C22semidirect
42. #2828C22semidirect
43. #2820C22semidirect
44. #2816C22semidirect
45. #2814C22semidirect
46. #2814C22semidirect
48. #2808C22semidirect
49. #2806C22semidirect
50. #2805C22semidirect
51. #2804C22semidirect
52. #2800C22semidirect
53. #2797C22semidirect
54. #2797C22semidirect
55. #2788C22semidirect
56. #2785C22semidirect
57. #2773C22semidirect
58. #2773C22semidirect
59. #2770C22semidirect
60. #2761C22semidirect
61. #2761C22semidirect
62. #2754C22semidirect
63. #2749C22semidirect
64. #2748C22semidirect
65. #2743C22semidirect
66. #2742C22semidirect
67. #2741C22semidirect
68. #2739C22semidirect
69. #2738C22semidirect
70. #2737C22semidirect
71. #2737C22semidirect
73. #2733C22semidirect
74. #2732C22semidirect
75. #2731C22semidirect
76. #2730C22semidirect
77. #2730C22semidirect
78. #2728C22semidirect
79. #2728C22semidirect
80. #2723C22semidirect
81. #2715C22semidirect
82. #2715C22semidirect
83. #2714C22semidirect
84. #2712C22semidirect
85. #2710C22semidirect
87. #2708C22semidirect
88. #2706C22semidirect
89. #2706C22semidirect
90. #2704C22semidirect
91. #2703C22semidirect
92. #2702C22semidirect
93. #2701C22semidirect
94. #2700C22semidirect
95. #2700C22semidirect
97. #2699C22semidirect
100. #2696C22semidirect
101. #2696C22semidirect
102. #2694C22semidirect
103. #2693C22semidirect
104. #2692C22semidirect
105. #2691C22semidirect
106. #2687C22semidirect
107. #2687C22semidirect
108. #2687C22semidirect
110. #2686C22semidirect
111. #2685C22semidirect
112. #2685C22semidirect
113. #2685C22semidirect
115. #2684C22semidirect
117. #2683C22semidirect
120. #2682C22semidirect
121. #2681C22semidirect
122. #2681C22semidirect
123. #2681C22semidirect
126. #2677C22semidirect
127. #2676C22semidirect
128. #2676C22semidirect
129. #2674C22semidirect
130. #2674C22semidirect
132. #2672C22semidirect
134. #2670C22semidirect
137. #2668C22semidirect
138. #2668C22semidirect
139. #2666C22semidirect
140. #2665C22semidirect
141. #2661C22semidirect
142. #2651C22semidirect
143. #2638C22semidirect
144. #2635C22semidirect
145. #2632C22semidirect
146. #2631C22semidirect
148. #2621C22semidirect
149. #2617C22semidirect
150. #2617C22semidirect
151. #2613C22semidirect
152. #2596C22semidirect
153. #2595C22semidirect
154. #2593C22semidirect
155. #2590C22semidirect
156. #2586C22semidirect
157. #2578C22semidirect
159. #2555C22semidirect
160. #2546C22semidirect
161. #2545C22semidirect
163. #2540C22semidirect
164. #2540C22semidirect
165. #2539C22semidirect
167. #2534C22semidirect
168. #2522C22semidirect
169. #2521C22semidirect
170. #2518C22semidirect
171. #2518C22semidirect
172. #2516C22semidirect
173. #2503C22semidirect
174. #2491C22semidirect
175. #2485C22semidirect
176. #2478C22semidirect
177. #2474C22semidirect
178. #2472C22semidirect
179. #2472C22semidirect
180. #2472C22semidirect
181. #2470C22semidirect
182. #2468C22semidirect
183. #2463C22semidirect
184. #2461C22semidirect
185. #2460C22semidirect
186. #2456C22semidirect
187. #2456C22semidirect
188. #2452C22semidirect
189. #2449C22semidirect
190. #2449C22semidirect
193. #2442C22semidirect
194. #2437C22semidirect
197. #2420C22semidirect
198. #2420C22semidirect
199. #2418C22semidirect
200. #2417C22semidirect
201. #2416C22semidirect
202. #2414C22semidirect
203. #2413C22semidirect
204. #2412C22semidirect
205. #2411C22semidirect
206. #2410C22semidirect
207. #2408C22semidirect
211. #2376C22semidirect
213. #2344C22semidirect
214. #2336C22semidirect
218. #2293C22semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#585772
#571682
#562892
#553142
#550702
#549532
#535952
#533912
#533572
#531762
#516292
#510672
#497712
#495622
#484992
#462372
#459622
#454542
#454532
#389552
#376552
#372692
#371502